Kinetic Theory

Step 1:
The pressure at the closed end of the tube is given by:
Step 2:
When the tube is held vertically, the pressure at the closed end is of mercury.
Step 3:
When the tube is held horizontally, the length of the air column changes due to the balance of pressures. The total length of the column is .

Step 1: Understanding the Concept:
The internal energy ( ) of an ideal gas depends on its temperature and degrees of freedom. For a mixture of non-reactive gases, the total internal energy is the sum of the internal energies of the individual gases. Formula: Where is the degrees of freedom, is number of moles, is gas constant, is temperature.
Step 2: Key Values:

• Monatomic gas ( ): moles.
• Diatomic gas ( at moderate temperature): moles.
• K.
• .

Step 3: Calculation:
Substitute values:
Step 4: Final Answer:
The total internal energy is 33.2 kJ.

• Specific heat capacity of liquid water (per mole) is approximately .
• Using , , which matches the known molar heat capacity of water.
• Therefore one mole of water has heat capacity approximately .

1. RMS speed:
2. Equate RMS speeds:
3.
4.
5. Convert to °C: C → closest to option 1 considering rounding.